The current price of a stock is $50. Every month, the stock price will rise by a factor of 1.2 or fall by a factor of 0.8; and a $1 risk-free investment will be worth $1.03. Dividends are paid as a proportion of the stock price. Which of the following $51-strike, six-month options has the highest value?
A) An American put when the stock pays no dividends.
B) A European put when the stock pays dividends at proportion 0.01 of the stock price.
C) An American call when the stock pays no dividends.
D) A European call when the stock pays dividends at proportion 0.01 of the stock price.

Question

Quizplus · Accepted Answer

Since the stock price rises or falls every month, an American option would be more valuable than a European option due to its flexibility. Also, an American call option benefits from the rising stock price, so it is likely to have the highest value. Dividends are paid as a proportion of the stock price, so a higher stock price leads to higher dividends. Thus, options with higher strike prices are likely to have lower values if the stock pays dividends. Since the stock pays a small proportion of dividends, the effect of the dividend is likely to be negligible. Therefore, the American call option with a strike price of $51 is the best choice.

The Current Price of a Stock Is $50